Attachments for syringes, carpules, or the like are generally known. They are also used as adapters and serve to provide an attachment means for a cannula or another device, for example an injection device or the like. For example, such attachments that are applied on an extension of the syringe, carpule, or the like are generally provided with an internal thread into which an insert of the cannula can be screwed. Attachments of the type discussed here are frequently configured as security- or tamper-evident-closures and include a first attachment part that is fixedly applied on a terminal extension of a syringe, a carpule, or the like and held there in a locking manner. In closures of this type, a cap is connected to the attachment body via a predetermined breaking line, which cap securely closes the free end of the extension and thus the interior of the syringe, carpule, or the like. If the cap is removed, the predetermined breaking line tears open so that it is irreversibly recognizable that the cap has been removed. Thus a protection against manipulation on the closure is also ensured. The extension includes a free end as well as, at a distance thereto, at least one depression introduced into the outer surface of the extension. An annular groove is preferably provided here wherein the attachment applied on the extension engages in a locking manner. After the placement of the attachment, a syringe, a carpule, or the like is often subjected to a sterilization process wherein, for example, hot steam is used. The high temperatures used during sterilization affect the material of the attachment, which engages under preload on the extension. It is thus possible that the material of the attachment will be compromised or even embrittled such that a secure hold of the attachment on the extension can no longer be ensured. It is also a disadvantage that attachments of the type discussed here, even if they are not subjected to a sterilization process under the effect of heat, are not always held securely enough on the extension, so that during transport or in the handling of the syringe, carpule, or the like. The attachment is inadvertently released. This is particularly undesirable if the attachment is configured as a tamper-evident closure and should close the interior of the syringe, carpule, or the like in a sterile manner. It has also been shown that a rotation of the attachment on the extension is often undesirable.